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Slovenia Team Selection Tests
2019 Slovenia Team Selection Test
1
1
Part of
2019 Slovenia Team Selection Test
Problems
(1)
Slovenia 2019 TST1 P1
Source: 2019 Slovenia 1st TST P1
2/18/2019
Let
A
B
C
ABC
A
BC
be a non-right isosceles triangle such that
A
C
=
B
C
AC = BC
A
C
=
BC
. Let
D
D
D
be such a point on the perpendicular bisector of
A
B
AB
A
B
, that
A
D
AD
A
D
is tangent on the
A
B
C
ABC
A
BC
circumcircle. Let
E
E
E
be such a point on
A
B
AB
A
B
, that
C
E
CE
CE
and
A
D
AD
A
D
are perpendicular and let
F
F
F
be the second intersection of line
A
C
AC
A
C
and the circle
C
D
E
CDE
C
D
E
. Prove that
D
F
DF
D
F
and
A
B
AB
A
B
are parallel.
TST
geometry